Try to see this equation as
$$
(xdy+ydx)+(xy)^2y^2dy
$$
to identify a useful change in variables resp. the separation into exact differentials.
$$
\frac{d(xy)}{(xy)^2}+y^2dy=0\implies -\frac3{xy}+y^3=C,
$$
which can be solved directly for $x$,
$$
x=\frac{3}{y^4-Cy},
$$
or while the solution for $y$ can only be given implicitly
$$
y^4-Cy=\frac3x.
$$